The Properties Of The Solutions Of Several Differential Equations In Complex Domain

In this paper, the value distribution theory and its basic methods are widely used,the properties of several kind of solution of differential equation are well researched.The article is divided into the following three chapters.First chapter, it mainly reviews the status of research on the theory of differentialequation of complex oscillation, as well as the research background of this article. Italso describes relevant notation, definitions and the relevant prior knowledge.Second chapter, by the index of solution of the zero point of convergence, indexof fixed point of convergence, and as well as from several aspects such as differentialpolynomial, we will come to study the properties of the solution. In the study of thenature of the solution, given the importance of the growth pole of solution, it is first tomake clear class of differential equations. We will analyze other similar results by theconclusions, we have got and then validated. Mainly discussing the relationshipbetween the class of homogeneous linear differential equations and their solutions offirst order, second order derivative and function. A class of homogeneous lineardifferential equation solution of the differential polynomial small function index pointsof convergence found that these problems are not affected by small functions. Inaddition, we also study the influence caused by a class of non-homogeneous lineardifferential equation with the fixed point and their first and second order derivative ofthe fixed point index of convergence.Third chapter, we will study the issue of the growth of solutions of the equationsunder the impact of a class of higher order differential equation of coefficient ofmeromorphic function, partial coefficient with finite deficient value.